Properties

Label 4002.j
Number of curves $1$
Conductor $4002$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 4002.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4002.j1 4002i1 \([1, 1, 1, 1735, 245063]\) \(577572497126639/26125579653696\) \(-26125579653696\) \([]\) \(10080\) \(1.2543\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 4002.j1 has rank \(1\).

Complex multiplication

The elliptic curves in class 4002.j do not have complex multiplication.

Modular form 4002.2.a.j

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} - 4 q^{7} + q^{8} + q^{9} + q^{10} + q^{11} - q^{12} + q^{13} - 4 q^{14} - q^{15} + q^{16} - 2 q^{17} + q^{18} + 2 q^{19} + O(q^{20})\) Copy content Toggle raw display